Understanding Analysis (2015, Corr. 2nd Printing 2016)

Overview

In the second edition of this fine text, Abbott (Middlebury College) left the body of the work largely intact and instead refined and expanded the list of problems and projects. For example, he added new projects involving the Weierstrass approximation theorem, the definition of the gamma function, and Euler's summation of 1/n2. The choice of topics is a happy combination of the essential and the interesting, all truly leading to an understanding of what analysis is and what questions it addresses, aided by the author's extraordinarily lucid exposition. The problem/project mix ranges from finger exercises to investigations that will test all students' understanding of deeper issues. In this reviewer's experience with perhaps six iterations of a course based on the first edition, students weaker and stronger all said that they believed Abbott's text had contributed mightily to the course. This is a worthy successor, highly appropriate for its times, to other classic go-to analysis texts, such as Walter Rudin's Principles of Mathematical Analysis (2nd ed., CH, Jun'64), Robert Bartle's The Elements of Real Analysis (2nd ed., CH, Apr'76), and Kenneth Ross's Elementary Analysis: The Theory of Calculus (2nd ed., 2013). Summing Up: Highly recommended. Upper-division undergraduates.--D. Robbins, emeritus, Trinity College (CT) Reprinted with permission of Choice, copyright 2015, American Library Association.